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A simple model for quotient types

Part of the Lecture Notes in Computer Science book series (LNCS,volume 902)

Abstract

We give an interpretation of quotient types within in a dependent type theory with an impredicative universe of propositions (Calculus of Constructions). In the model, type dependency arises only at the propositional level, therefore universes and large eliminations cannot be interpreted. In exchange, the model is much simpler and more intuitive than the one proposed by the author in [10]. Moreover, we interpret a choice operator for quotient types that, under certain restrictions, allows one to recover a representative from an equivalence class. Since the model is constructed syntactically, the interpretation function from the syntax with quotient types to the model gives rise to a procedure which eliminates quotient types by replacing propositional equality by equality relations defined by induction on the type structure (“book equalities”).

Keywords

  • Type Theory
  • Inductive Type
  • Choice Operator
  • Interpretation Function
  • Terminal Object

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supported by a EU HCM fellowship, contract number ERBCHBICT930420

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© 1995 Springer-Verlag Berlin Heidelberg

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Hofmann, M. (1995). A simple model for quotient types. In: Dezani-Ciancaglini, M., Plotkin, G. (eds) Typed Lambda Calculi and Applications. TLCA 1995. Lecture Notes in Computer Science, vol 902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014055

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  • DOI: https://doi.org/10.1007/BFb0014055

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59048-4

  • Online ISBN: 978-3-540-49178-1

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